Solve [3/4*0.001t^4-1/3*0.01t^3-1/20.3t^2+4t]_0^12

$$[ \frac { 3 } { 4 } \cdot 0.001 t ^ { 4 } - \frac { 1 } { 3 } \cdot 0.01 t ^ { 3 } - \frac { 1 } { 2 } 0.3 t ^ { 2 } + 4 t ] _ { 0 } ^ { 12 }$$

Evaluate

$$\frac{3t^{4}}{4000}-\frac{t^{3}}{300}-\frac{3t^{2}}{20}+4t$$

Solution Steps

Multiply \frac{3}{4} and 0.001 to get \frac{3}{4000}.

$$\frac{3}{4000}t^{4}-\frac{1}{3}\times 0.01t^{3}-\frac{1}{2}\times 0.3t^{2}+4t$$

Multiply \frac{1}{3} and 0.01 to get \frac{1}{300}.

$$\frac{3}{4000}t^{4}-\frac{1}{300}t^{3}-\frac{1}{2}\times 0.3t^{2}+4t$$

Multiply \frac{1}{2} and 0.3 to get \frac{3}{20}.

$$\frac{3}{4000}t^{4}-\frac{1}{300}t^{3}-\frac{3}{20}t^{2}+4t$$

Factor

$$\frac{t\left(9t^{3}-40t^{2}-1800t+48000\right)}{12000}$$

Solution Steps

Multiply \frac{3}{4} and 0.001 to get \frac{3}{4000}.

$$factor(\frac{3}{4000}t^{4}-\frac{1}{3}\times 0.01t^{3}-\frac{1}{2}\times 0.3t^{2}+4t)$$

Multiply \frac{1}{3} and 0.01 to get \frac{1}{300}.

$$factor(\frac{3}{4000}t^{4}-\frac{1}{300}t^{3}-\frac{1}{2}\times 0.3t^{2}+4t)$$

Multiply \frac{1}{2} and 0.3 to get \frac{3}{20}.

$$factor(\frac{3}{4000}t^{4}-\frac{1}{300}t^{3}-\frac{3}{20}t^{2}+4t)$$

Factor out \frac{1}{12000}.

$$\frac{9t^{4}-40t^{3}-1800t^{2}+48000t}{12000}$$

Consider 9t^{4}-40t^{3}-1800t^{2}+48000t. Factor out t.

$$t\left(9t^{3}-40t^{2}-1800t+48000\right)$$

Rewrite the complete factored expression. Polynomial 9t^{3}-40t^{2}-1800t+48000 is not factored since it does not have any rational roots.

$$\frac{t\left(9t^{3}-40t^{2}-1800t+48000\right)}{12000}$$